Rutgers MAMLS 2019

Department of Mathematics, Rutgers University

Schedule.

Day 1. Friday November 1st.

All Friday talks will take place in Hill Center, Busch Campus (check the rooms)

ATTENTION: Please do not be scared by the location, after all Francis Urquhart will also be there!

1:00-2:00 Sandra Mueller (University of Vienna) Room 005 (basement of Hill Center)

Title: Sealed Trees and the Perfect Subtree Property for Weakly Compact Cardinals

2:30-3:30 Christian Rosendal (UIC) Room 005 (basement of Hill Center)

Title: Continuity of universally measurable homomorphisms.

4:00-5:00 Justin Moore (Cornell) Room 705 (crosslisted as the Math Colloquim Talk)

Title: Groups of piecewise linear homeomorphisms

Abstract: Piecewise linear homeomorphisms of the unit interval "have been a source of groups with interesting properties in which calculations are practical." Recently a program has been initiated to understand the collective structure of these groups under the embeddability relation. I will discuss a number of recent results and conjectures along these lines. Remarkably the ordinal $\epsilon_0$ makes an appearance, suggesting that logic may provide important tools and insight into this program.

Day 2. Saturday November 2nd.

All Saturday talks will take place Murray Hall - Room 111 (College Avenue campus).

Something to cheer you up: If you have not enjoyed the company of our esteem collegaue Francis Urquhart in the dark basement of Hill Center, then we certainly hope that you will enjoy the rich colonial history of our College Avenue campus. Just make sure you don't wander off too far.

9:00am--10am Saharon Shelah (Rutgers, Hebrew University)

Title: Interpolation for non-first order logics

10:30am--11:30am James Freitag (UIC)

Title: Model theory, automorphic functions, and differential equations

Abstract: Given an analytic function, $f: \mathbb C^n \rightarrow \mathbb C^n$, we call an algebraic variety $V \subset \mathbb C^n$ bi-algebraic for $f$ if $f(V)$ is algebraic. Most varieties are not bi-algebraic, should be special and reveal certain aspects of the geometry of $f$. We will talk about several recent approaches to bi-algebraicity problems through model theory and differential equations. We will also talk about how bi-algebraicity problems are related to several number theoretic applications - special points conjectures and transcendence problems. The results we discuss center around automorphic functions, which we will introduce in the talk.

11:45am--12:45pm Assaf Shani (CMU, Harvard)

Title: Above countable products of countable equivalence relations.

Abstract: We study some Borel equivalence relations very low in the hierarchy, above the countable products of countable Borel equivalence relations. Clemens and Coskey have recently defined new jump operations as follows. Given an equivalence relation E on X and a countable group G, the G-jump of E is defined on the product space X^G by declaring x and y equivalent if and only if there is some g in G such that after shifting x by g, it is pointwise E-equivalent to y. Given a countable Borel equivalence relation E they showed that the G-jumps of E are above the infinite power E^\omega in the Borel reducibility hierarchy, and asked whether the F_2 jump is above the Z-jump. We show in fact that the Z^2-jump is strictly above the Z-jump. This should be viewed in contrast to the fact that a countable Borel equivalence relation induced by an action of Z^2 is Borel reducible to a Z-action. We will discuss how to translate questions about Borel reducibility to questions about definability in symmetric models. The proof then relies on analyzing symmetric models in which very weak forms of choice fail.

2:30pm--3:30pm Steve Jackson (University of North Texas)

Title: Determinacy, Equivalence Relations, and Group Actions.

Abstract: We investigate when \Gamma-determinacy for E-invariant sets implies \Gamma determinacy. Our main result implies this for shift actions and reasonable \Gamma, and involves introducing a weak form of amenability for groups.

4:00pm-5:00pm Pierre Simon (UC Berkeley)

Title: Towards classification theory for NIP

Day 2. Sunday November 3rd.

All Sunday talks will take place at Murray Hall - Room 111 (College Avenue campus).

9:30am--10:30am John Steel (UC Berkeley)

Title: Mouse pairs and Suslin cardinals

11:00am--12 am Chris Laskowski (University of Maryland, CP)

Title: Ranks vs. non-structure in atomic classes

While graduate students, young researchers, female mathematicians and members of under-represented groups are particularly encouraged to apply for travel support, it should be stressed that any participants without their own sources of funding are eligible to apply. Requests will be handled on a case-by-case basis within the limits of the budget. Please send an email to Russell.Miller @ qc.cuny.edu